Question

An object is placed $20cm$ in front of a block of glass $10cm$ thick and its farther surface is silvered. The image is formed $23.2cm$ behind the silvered face. Determine the refractive index of the glass.

Answer 1

Given: An object is placed 20 cm in front of a block of glass 10 cm thick and its farther surface is silvered. The image is formed 23.2 cm behind the silvered face.

To find the refractive index of the glass.

Solution:

We know,

Refractive index $\mu =\frac{\text{Real depth}}{\text{apparent depth}}$

Given real depth = object distance in front of the block = 20cm

Let the apparent depth be $x$

Thus, $\mu =\frac{20}{x}$

Silvered surface acts as mirror.

Thus, to get the image 23.2 cm behind, the object should be 23.2cm in front. (plane mirror property)

Therefore, $x+\text{thickness of glass}=23.2⟹x+10=23.2⟹x=13.2cm$

Therefore, $\mu =\frac{20}{13.2}=1.5$

is the required refractive index of the glass.